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Can someone suggest some, that give close to 2% or better return?
One downside with AMEX is that it seems fewer and fewer merchants are accepting them. And from a merchant's perspective, I complete understand why (I'm made several anti-AMEX posts here from the merchant's perspective).
So we also have a couple of non-AMEX rewards cards to use with merchants that don't accept AMEX. Our Office Depot Visa gives 1-2% cashback and 5% cashback for purchases at Office Depot. We don't need office supplies very often (and usually buy at Staples anyway because of convenience plus AMEX gives, or at least gave, an extra cashback there). Also have a Capital One card that gives miles, although rarely use it- prefer the cash to miles.
For further research, CitiBank has a huge array of different cards. Have fun mixing and matching cashback, miles, "thank you" points, etc. You can also get more points for opening up different accounts (savings, checking, etc.) with them.
I am getting 4% cash on purchases using AMEX Platinum.
For petrol I use AMEX Nectar and get 4 Nectar points per £1, instead of 1 (you need to present a Nectar card & AMEX Nectar when paying) this one is unlimited and indefinete.
Also if you use an online cashback co-op like quidco, you can get another 2-4% for many purchases.
If you are interested in this card it is offered by Chase and is their British Airways Reward Card